# Model Fit Statistics for an Estimated Latent Variable Model A function to compute model fit statistics for latent variable models estimated with lamle. Currently only computes the standardized root mean square residuals (SRMSR) from the model-implied correlation matrix based on the estimated model parameters and the sample correlation matrix. ```r lamle.fit(obj, obs, N = NULL, z = NULL, seed = NULL, use = "complete", residmat = FALSE) ``` ## Arguments - `obj`: An estimated model from function lamle. - `obs`: The observed data matrix, with missing values coded as NA. Ordinal data must be coded as successive integers starting from 1. - `N`: A numeric scalar indicating the multiplier of the sample size in the data to use when computing the model fit statistics. - `z`: An optional matrix of latent variable values to use when computing the model fit statistics. - `seed`: The seed to use when simulating data. - `use`: A character vector indicating how the correlaion matrix used for the SRMSR statistic should be estimated. See function cor() for details. - `residmat`: Optional argument to return the full residual correlation matrix. ## Returns A numeric vector with fit statistics. ## Author(s) Björn Andersson and Shaobo Jin ## References Andersson, B., and Xin, T. (2021). Estimation of latent regression item response theory models using a second-order Laplace approximation. **Journal of Educational and Behavioral Statistics**, 46(2) 244-265. Jin, S., Noh, M., and Lee, Y. (2018). H-Likelihood Approach to Factor Analysis for Ordinal Data. **Structural Equation Modeling: A Multidisciplinary Journal**, 25(4) , 530-540. Shun, Z., and McCullagh, P. (1995). Laplace approximation of high dimensional integrals. **Journal of the Royal Statistical Society: Series B (Methodological)**, 57(4) , 749-760. ## Examples ```r ##### Load required package. library(mvtnorm) ##### Generate ordinal data from the GPCM ##### ##### Item parameter generation set.seed(123) GPCMa <- runif(10, 0.8, 2) GPCMb <- vector("list", 10) for(i in 1:10) GPCMb[[i]] <- -c(runif(1, -3, -2), runif(1, -1.5, -0.5), runif(1, 0, 1), runif(1, 1.5, 2.5)) GMCMa2d <- matrix(0, nrow = 10, ncol = 2) GMCMa2d[1:5, 1] <- GPCMa[1:5] GMCMa2d[6:10, 2] <- GPCMa[6:10] ##### Latent variables in two groups n <- 200 set.seed(1234) covmat2d <- diag(rep(1, 2)) covmat2d[!diag(2)] <- 0.6 latmat2dA <- rmvnorm(n, c(0, 0), covmat2d) latmat2dB <- rmvnorm(n, c(1, 1), covmat2d) ##### Observed data set.seed(12345) dataGPCM2d <- matrix(NA, nrow = 2 * n, ncol = 10) dataGPCM2d[1:n, ] <- DGP(GMCMa2d, GPCMb, rep("GPCM", 10), latmat2dA) dataGPCM2d[(n + 1):(2 * n), ] <- DGP(GMCMa2d, GPCMb, rep("GPCM", 10), latmat2dB) ##### Setup two-dimensional independent-clusters model mydim2d <- matrix(NA, nrow = 10, ncol = 2) mydim2d[1:5, 1] <- 1 mydim2d[6:10, 2] <- 1 ##### Lap(2) estLap2 <- lamle(y = dataGPCM2d[1:n,], model = mydim2d, modeltype = rep(c("GPCM", "GRM"), 5), method = "lap", accuracy = 2, optimizer = "BFGS", inithess = "crossprod") lamle.fit(estLap2, dataGPCM2d[1:n,], N = 10) ```

lamle.fit function